Optical frequency combs with equally-spaced laser lines that are strictly determined by the laser repetition-rate and the carrier-envelope-offset frequency have become powerful tools for exploring many physical phenomena to unprecedented levels. By stabilizing both frequencies (repetition-rate and carrier-envelope-offset frequencies), one can not only identify the absolute frequency of each line and achieve extremely high precision and stability in frequency metrology applications [T. Udem, et al., “Optical frequency metrology,” Nature 416, 233-237 (2002)], but also use these frequencies for additional applications such as resonant enhancement of optical pulses [M. J. Thorpe, et al., “Broadband cavity ringdown spectroscopy for sensitive and rapid molecular detection,” Science 311, 1595 (2006)] and calibration of astronomical spectrographs (astro-comb). [M. T. Murphy, et al., “High-precision wavelength calibration with laser frequency combs,” Mon. Not. R. Astron. Soc. 380, 839-847 (2007); and C.-H. Li, et al., “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm/s,” Nature 452, 610 (2008)]. In both of the later applications, optical filter cavities are incorporated, and their performance significantly affects the practicability of these applications. Brief descriptions of applications that use filter cavities are provided, below.
First, for an enhancement cavity, the equally-spaced spectral lines from a frequency comb are coupled into a high-finesse optical cavity with its free-spectral range (FSR) matched to the laser repetition rate. In this way, all the frequency components are in phase, which constructively enhance the resonant pulse circulating inside the cavity.
Second, in high-precision wavelength calibration with laser frequency combs (or astro-comb) application, the optical cavities are used to increase the comb spacing, which enables the calibration of lower resolution spectrographs using lasers with lower fundamental repetition rates. In this case, the cavity's free-spectral range is a multiple of the source-comb spacing, and the cavity acts as a filter that selectively blocks unwanted lines and passes those aligned with the cavity's transmission peaks. Such a filtered comb with increased line spacing has become an advantageous calibration tool for astronomical spectrographs, which holds promise for finding exoplanets similar to the Earth.
Optical filter cavities are typically formed by two or more mirrors of high reflectivity. In the ideal case, when these mirrors are carefully aligned, the Fabry-Perot (FP) cavity will have periodic transmission peaks in the frequency domain with their spacing determined by the physical distance of the round-trip path. Therefore, by carefully adjusting this distance, one should theoretically be able to match these transmission peaks to all of the femtosecond laser frequency comb lines since they are also equally spaced. However, in practice, the cavity's resonances undergo a wavelength-dependent shift due to the phase error accumulated from the dispersion of cavity mirrors and the intracavity material. As a result, the mismatch between cavity's transmission peaks and the input laser comb lines leads to dropout of comb-teeth, which may greatly reduce the overall spectral width coupled into the cavity and therefore imposes practical limitations to the aforementioned applications. In experiments utilizing the resonant field enhancement, the cavity bandwidth determines the transform-limited pulse duration as well as the peak intensity of the circulating pulses. In high-precision wavelength calibration, this mismatch limits the spectral coverage of the comb lines which limits the sensitivity to small frequency drifts. Therefore, development of broadband, dispersion-free cavity mirrors is highly advantageous. The design described herein can successfully extend the bandwidth of optical cavities over traditional designs.
The traditional design of such cavities is based on Bragg-stack mirrors (BSMs), as shown in FIG. 1; and a plot of the mirror penetration depth as a function of wavelength for this design is provided in FIG. 2. Although BSMs are typically high reflectors with moderate bandwidth, not all wavelengths are reflected from the same depth of the structure. Consequently, only a small portion of the spectrum near the center of the high-reflectivity region has negligible dispersion, leading to a very limited bandwidth of the resulting Fabry-Perot cavity. This bandwidth degradation becomes even worse when the dispersion from intracavity materials is taken into account. As a result, the cavity is placed in vacuum if the cavity length is too long such that the air dispersion is eliminated.